Optimal vibration control of half-car suspension system integrated with human biodynamic model using Gray Wolf Optimizer

Increasing demands for ride comfort, vibration attenuation, and occupant health protection in modern transportation systems have motivated the development of advanced suspension control strategies capable of simultaneously addressing vehicle dynamic behavior and human biodynamic response under varying operating conditions. This paper presents a comprehensive framework for active suspension systems through the integrated analysis of vehicle dynamics and occupant biodynamic characteristics. A sophisticated integrated model is developed comprising a five-degree-of-freedom half-car longitudinal vehicle model with seat dynamics and an 11-degree-of-freedom physical driver model. A Linear Quadratic Regulator (LQR) controller is designed for active suspension control, followed by the application of Gray Wolf Optimization (GWO) algorithm to optimize the LQR weighting matrices through a multi-objective approach. Comparative analysis under sinusoidal road excitation (5 Hz, 0.01 m amplitude) at 60 km/h demonstrates significant performance improvements. The standard LQR controller achieves substantial vibration reduction: 48.9% in sprung mass displacement, 48.8% in sprung mass acceleration, and 59.6% in seat acceleration. The GWO-optimized LQR controller demonstrates remarkable performance within the adopted simulation framework, with reductions exceeding 99.99% for key vehicle parameters including sprung mass displacement (99.99997%) and acceleration (99.99997%). Human vibration analysis reveals critical insights, with the optimized controller achieving reductions of 59.1%–59.6% for torso and pelvic regions using LQR alone, and 99.99%–99.996% across all body segments with LQR + GWO optimization. Furthermore, robustness evaluations under ISO 8608:2016 stochastic road excitations demonstrate that the proposed controller maintains effective vibration suppression performance across a broad range of road roughness categories (classes A–D) and vehicle operating conditions, confirming its applicability under realistic random road environments. The research establishes significant improvement relative to LQR configuration, validating the effectiveness of metaheuristic optimization for integrated vehicle-human systems.